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Modular Multiplicative Inverse — result sheet
Find the integer that multiplies a value to 1 modulo a coprime modulus.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: The inverse a^-1 modulo m satisfies a x a^-1 = 1 (mod m) when gcd(a, m) = 1.
The extended Euclidean algorithm supplies an exact inverse when the value and modulus are coprime. The result is normalized to the interval from 0 through m - 1.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Value a — minimum -1000000000; maximum 1000000000
- Modulus — minimum 2; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Value a | 3 |
| Modulus | 11 |
The inverse of 3 modulo 11 is 4.
Assumptions and limits
- The modulus is a positive integer at least 2.
- An inverse exists only when gcd(a, modulus) = 1.
- The result is a residue class representative, not a decimal reciprocal.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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